Bipedal robotic mechanisms are unstable due to the unilateral contact passive joint between the sole and the ground. Hierarchical control layers are crucial for creating walking patterns, stabilizing locomotion, and ensuring correct angular trajectories for bipedal joints due to the system’s various degrees of freedom. This work provides a hierarchical control scheme for a bipedal robot that focuses on balance (stabilization) and low-level tracking control while considering flexible joints. The stabilization control method uses the Newton–Euler formulation to establish a mathematical relationship between the zero-moment point (ZMP) and the center of mass (COM), resulting in highly nonlinear and coupled dynamic equations. Adaptiv

This paper deals with an analytical study of the flow of an incompressible generalized Burgers’ fluid (GBF) in an annular pipe. We discussed in this problem the flow induced by an impulsive pressure gradient and compare the results with flow due to a constant pressure gradient. Analytic solutions for velocity is earned by using discrete Laplace transform (DLT) of the sequential fractional derivatives (FD) and finite Hankel transform (FHT). The influences of different parameters are analyzed on a velocity distribution characteristics and a comparison between two cases is also presented, and discussed in details. Eventually, the figures are plotted to exhibit these effects.

This paper presents a nonlinear finite element modeling and analysis of steel fiber reinforced concrete (SFRC) deep beams with and without openings in web subjected to two- point loading. In this study, the beams were modeled using ANSYS nonlinear finite element
software. The percentage of steel fiber was varied from 0 to 1.0%.The influence of fiber content in the concrete deep beams has been studied by measuring the deflection of the deep beams at mid- span and marking the cracking patterns, compute the failure loads for each deep beam, and also study the shearing and first principal stresses for the deep beams with and without openings and with different steel fiber ratios. The above study indicates that the location of openings an

In this study, a three-dimensional finite element analysis using ANSYS 12.1 program had been employed to simulate simply supported reinforced concrete (RC) T-beams with multiple web circular openings subjected to an impact loading. Three design parameters were considered, including size, location and number of the web openings. Twelve models of simply supported RC T-beams were subjected to one point of transient (impact) loading at mid span. Beams were simulated and analysis results were obtained in terms of mid span deflection-time histories and compared with the results of the solid reference one. The maximum mid span deflection is an important index for evaluating damage levels of the RC beams subjected to impact loading. Three experi

  Theoretical study computerized has been carried out in field electron optics , to design electrostatic unipotential lens , the inverse problem is important method in the design of electrostatic lenses by suggesting an axial electrostatic potential distribution using polynomial function. The paraxial –ray equation is solved to obtain the trajectory particles that satisfy the suggested potential function. In this research , design electrostatic unipotential lens three-electrode accelerating and decelerating L=5 mm operated under finite and infinite magnification conditions. The electrode shape of the electrostatic lens was then determined from the solution of the Laplace's equation's. the results showed low values of spherica